# Algebraic Expressions

Okay, let's clear this up:

An **equation** is a *complete* mathematical sentence that includes a sign of equality (like an equal sign).

An **expression** is **not** a mathematical sentence; it is a mathematical phrase because *it doesn't have an equal sign.*

Expression | Equation |

5 + 2 | 5 + 2 = 7 |

3x | 3x = 15 |

4(5 + 8x) | 4(5 + 8x) = -44 |

Let's break it down further.

An expression is made up of terms. **Terms** are each separate values in an expression. They can be separated by operations, like plus and minus signs.

There are three parts of most expressions: the variable, constant, and coefficient.

**Variable**: an unknown or changing number. Often represented by “x”.**Constant**: a number that doesn’t change**Coefficient**: the number that is multiplied by the variable

## Names for algebraic expressions

monomial | 1 Term | xy |

binomial | 2 Terms | xy - 2x |

trinomial | 3 Terms | xy - 2x + 3y |

quadnomial | 4 Terms | xy - 2x + 3 y – 1 |

Here is a chart of common phrases.

Common Words and Phrases for: | ||||
---|---|---|---|---|

Add | Subtract | Multiply | Divide | Equals |

plus add sum more than in addition to greater than total and | difference subtract less than take away | product of times twice (×2) factor | divided by quotient split share distribute | is |

In these translations we will use the letter x to represent the variable, though any letter, symbol, or emoticon would work. Smiley faces and hearts, anyone?

Expression in Words | Expression in Symbols |
---|---|

a number increased by twelve | x + 12 |

the sum of twice a number and six | 2x + 6 |

eighty less than a number | x – 80 |

twenty-eight split in half | 28 ÷ 2 |

the product of a number and seven | 7x |

the quotient of a number and four | x ÷ 4 |

five greater than three times a number | 3x + 5 |

a number distributed evenly among six | x ÷ 6 |

the total of forty and a number | 40 + x |

three times the total of a number and five | 3(x + 5) |

Equation in Words | Equation in Symbols |
---|---|

A number is negative ten. | x = -10 |

A number plus two is eight. | x + 2 = 8 |

The difference between a number and seven is negative three. | x – 7 = -3 |

One less than twice a number is seventeen. | 2x – 1 = 17 |

Twelve is the product of a number and three. | 12 = 3x |

Half of a number is twenty. | x × ½ = 20 or ½x = 20 |

A number is equal to the sum of twice the number and negative three. | x = 2x + -3 |

**Look Out:** be very careful with "less than". Three less than a number is translated as "x – 3". The reverse of that, "3 – x" would be a number less than three.